Conventional medical x-ray imaging devices employ absorption information to probe the interior structure of imaged objects. While generally good contrast between highly attenuating (e.g., hard) and weakly attenuating (e.g., soft) materials is observed, the separation between soft-tissue materials can be difficult because of a low relative contrast. For example, the low-contrast soft tissue materials include, but are not limited to vessels, cartilages, lungs, and breast tissues, which provide poor contrast in comparison to highly attenuating bone structures. In the recent years, interferometric x-ray imaging devices have been introduced to address soft-tissue imaging. In addition to conventional absorption, such devices can use the wave nature of x-ray radiation to measure diffraction of x-rays traversing the imaged object. As an electromagnetic wave, the x-ray can be characterized by its frequency, amplitude, and phase. When an x-ray, as an electromagnetic wave, penetrates a medium, its amplitude is attenuated and phase is shifted. The material dependent index of refraction can be represented as equation (1) below:n=1−δ+iβ,  (1)where the imaginary part β contributes to the attenuation of the amplitude and the real part δ (refraction index decrement) is responsible for the phase shift. While the interferometer type of imaging devices can measure both β and δ terms, the conventional x-ray imaging devices can detect only β. It is known that β and δ are proportional to atomic scattering factors. For example, for a compound of density ρ the refractive index, shown in equation (1), can be expressed in terms of the atomic scattering factors f1 and f2 as equation (2) below:
                              n          ≅                      1            -                                                                                r                    e                                    ⁢                                      N                    a                                    ⁢                                      λ                    2                                    ⁢                  ρ                                                  2                  ⁢                                                                          ⁢                  π                                            ⁢                              (                                                      ∑                    k                                    ⁢                                                                          ⁢                                                            x                      k                                        ⁡                                          (                                                                        f                                                      1                            ,                            k                                                                          +                                                  if                                                      2                            ,                            k                                                                                              )                                                                      )                            ⁢                              /                            ⁢                              (                                                      ∑                    k                                    ⁢                                                                          ⁢                                                            x                      k                                        ⁢                                          A                      k                                                                      )                                                    ,                            (        2        )            where re, Na, λ, and ρ are the electron radius, Avogadro number, photon wavelength, and effective density of compound, respectively. The summation is taken over the relative concentrations xk of each of the chemical elements of atomic mass Ak comprising the compound. Using equation (2), it can be shown that δ (rad/cm units) is about 103 to 104 times larger than β (1/cm units). This provides a potential for imaging soft-tissue materials with higher contrast.
To date, several phase contrast imaging (PCI) techniques have been explored including: 1) the interferometer technique, 2) the diffraction-enhanced imaging (DEI) technique, and 3) the free-space propagation technique. However, there are various practical problems associated with all three techniques. In the case of crystal interferometers and diffractometers, high temporal coherence (i.e., a high degree of monochromaticity) is required, which, in result, limits the application to a synchrotron radiation or a well defined monochromatic radiation source. In addition to requirement of synchrotron source, the use of multi-hole collimator in DEI limits the achievable spatial resolution and increases the acquisition time. The free-space propagation technique can be limited in efficiency because of a requirement of high spatial coherence, which only can be obtained from an x-ray source with a very small focal spot size, or large propagation distance.
Further, grating based interferometer devices can be used for differential phase contrast imaging. Such imaging devices can include standard broadband x-ray source, beam shaping assembly including a collimator, three gratings (source G0, phase G1, and absorption G2 gratings), and x-ray detector; where the three gratings are positioned in such a way that their plane and the grating bars are aligned to each other. Alternatively, a microfocus X-ray source or synchrotron radiation source can be used instead of grating G0 and a large incoherent X-ray source.
Commonly accepted acquisition techniques for grating based PCI systems can use a controlled displacement during imaging of one of the three gratings relative to each other over the period of grating structure of absorption grating G2, which is typically few microns (e.g., 2 μm). Such an acquisition technique can be referred to as a phase stepping technique. Typical value of one displacement or step in such an acquisition is in the order of few hundred nanometers (e.g., 250 nm-500 nm). Although piezoelectric actuators, which can be used for grating displacement, can reach 10's of nanometer precision, the piezoelectric actuators are not linear (e.g., the relationship between displacement, x, and applied voltage V is not linear). To obtain high quality image reconstruction, the displacement Δx needs to stay constant during stepping, which requires unequal voltage increments, ΔV, at each step. Repeatability or optimization of such a system configuration can require thorough calibration, which prescribes the nominal voltage values at each step. Alternatively, a position sensitive feedback system can be used to linearize the voltage versus displacement characteristic. In addition, thermal expansion and/or compression of flexures holding the stepping grating can easily result in displacement of over a hundred of nanometers per Celsius degree. Thus, good thermal stability during an image acquisition time can be required. Accordingly, there is a long felt need for improvements to grating based PCI systems and/or methods for using the same.